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Chapter 1: Q 16. (page 50)

Write the standard form of the equation and the general form of the equation of each circle of radius rand center h,k.

Graph each circle.

r=4;(h,k)=(2,-3)

Short Answer

Expert verified

Standard form of the circle is (x-2)2+(y+3)2=42

General form of the circle isx2+y2-4x+6y-3=0

Graph is as follows:

Step by step solution

01

Step 1. Given information

It is given thatr=4;(h,k)=(2,-3)

02

Step 2. Standard form of the circle

The standard form the circle with center h,kand radius ris (x-h)2+(y-k)2=r2

It is given that r=4and h,k=2,-3.

Therefore, the standard form of the circle is

(x-2)2+(y-(-3))2=42(x-2)2+(y+3)2=42

03

Step 3. General form of the circle

The general form of the circle is obtained by simplifying the standard form:

x2-4x+4+y2+6y+9=16x2+y2-4x+6y+13=16

Subtract 16from both sides

x2+y2-4x+6y-3=0

04

Step 4. Graph of the circle

Graph of the circle is as follows:

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